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December 30, 2018 03:55
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Simulation of War, the card game
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Init Packages" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"using Random, DataStructures, Plots, Statistics" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Define `struct` or type for a game of war, `WarGame`" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"mutable struct WarGame\n", | |
" d1::CircularBuffer{UInt8} # d for deck\n", | |
" d2::CircularBuffer{UInt8} # d for deck\n", | |
" z1::CircularBuffer{UInt8} # z for discard\n", | |
" z2::CircularBuffer{UInt8} # z for discard\n", | |
"\n", | |
" round_count::UInt64\n", | |
"end" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Define constructor for `WarGame`" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"WarGame" | |
] | |
}, | |
"execution_count": 3, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"# make unshuffled, initial deck\n", | |
"jokers = true\n", | |
"ONE_SUIT = collect(UInt8, 2:14) # (2 through Ace)\n", | |
"FOUR_SUITS = repeat(ONE_SUIT, 4)\n", | |
"JOKER_CARDS = jokers ? UInt8[15, 15] : UInt8[]\n", | |
"UNSHUFFLED_DECK = cat(\n", | |
" FOUR_SUITS, # (2 through Ace) * 4 suits\n", | |
" JOKER_CARDS, # 0 or 2 Jokers\n", | |
" dims=1\n", | |
")\n", | |
"\n", | |
"function WarGame(; jokers=true)\n", | |
" d1 = CircularBuffer{UInt8}(length(UNSHUFFLED_DECK))\n", | |
" d2 = CircularBuffer{UInt8}(length(UNSHUFFLED_DECK))\n", | |
" z1 = CircularBuffer{UInt8}(length(UNSHUFFLED_DECK))\n", | |
" z2 = CircularBuffer{UInt8}(length(UNSHUFFLED_DECK))\n", | |
"\n", | |
" half = Int(length(UNSHUFFLED_DECK)/2)\n", | |
" deck_perm = randperm(length(UNSHUFFLED_DECK))\n", | |
" for ix=deck_perm[ 0 .+ (1:half)]; push!(d1, UNSHUFFLED_DECK[ix]); end\n", | |
" for ix=deck_perm[ half .+ (1:half)]; push!(d2, UNSHUFFLED_DECK[ix]); end \n", | |
"\n", | |
" round_count = UInt64(0)\n", | |
"\n", | |
" WarGame(d1, d2, z1, z2, round_count)\n", | |
"end" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Define function to play a single game of war\n", | |
"* The return value is the number of round played in a game of war" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"play_war1 (generic function with 1 method)" | |
] | |
}, | |
"execution_count": 4, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"function play_war1()\n", | |
" g = WarGame()\n", | |
" while length(g.d1) > 0 && length(g.d2) > 0\n", | |
" # play single round of war \n", | |
" while length(g.d1) > 0 && length(g.d2) > 0\n", | |
" # @show g.d1[1], g.d2[1]\n", | |
" if g.d1[1] > g.d2[1] # player 1 wins hand\n", | |
" push!(g.z1, popfirst!(g.d1))\n", | |
" push!(g.z1, popfirst!(g.d2))\n", | |
"\n", | |
" elseif g.d1[1] < g.d2[1] # player 2 wins hand\n", | |
" push!(g.z2, popfirst!(g.d2))\n", | |
" push!(g.z2, popfirst!(g.d1))\n", | |
"\n", | |
" elseif g.d1[1] == g.d2[1] # tie\n", | |
" ix_check = 3\n", | |
" L1 = length(g.d1)\n", | |
" while all(ix_check .<= (length(g.d1) ,length(g.d2)))\n", | |
" if g.d1[ix_check] > g.d2[ix_check]\n", | |
" for ix=1:ix_check; push!(g.z1, popfirst!(g.d1)); end\n", | |
" for ix=1:ix_check; push!(g.z1, popfirst!(g.d2)); end\n", | |
" break\n", | |
" elseif g.d1[ix_check] < g.d2[ix_check]\n", | |
" for ix=1:ix_check; push!(g.z2, popfirst!(g.d2)); end\n", | |
" for ix=1:ix_check; push!(g.z2, popfirst!(g.d1)); end\n", | |
" break\n", | |
" elseif g.d1[ix_check] == g.d2[ix_check]\n", | |
" ix_check += 1\n", | |
" end\n", | |
" end\n", | |
"\n", | |
" # if there was no movement, then just break\n", | |
" if length(g.d1) == L1\n", | |
" break\n", | |
" end\n", | |
" end # 3 clause win1 / win2 / tie\n", | |
" # println(\"$(length(g.d1)), $(length(g.d2)), $(length(g.z1)), $(length(g.z2))\")\n", | |
" end # single round\n", | |
"\n", | |
" # force potential leftovers from d1 to z1 and d2 to z2\n", | |
" for ix=1:length(g.d1); push!(g.z1, popfirst!(g.d1)); end\n", | |
" for ix=1:length(g.d2); push!(g.z2, popfirst!(g.d2)); end\n", | |
"\n", | |
" # shuffle z1 to d1 and z2 to d2\n", | |
" for ix=randperm(length(g.z1)); push!(g.d1, g.z1[ix]); end\n", | |
" for ix=randperm(length(g.z2)); push!(g.d2, g.z2[ix]); end\n", | |
"\n", | |
" # empty z1 and z2 after they've been shuffled back to d1 and d2\n", | |
" empty!(g.z1)\n", | |
" empty!(g.z2)\n", | |
"\n", | |
" g.round_count += 1\n", | |
"\n", | |
" # println(\"$(g.round_count): $(length(g.d1)), $(length(g.d2)), $(length(g.z1)), $(length(g.z2))\")\n", | |
" end # single game\n", | |
" return g.round_count\n", | |
"end" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Use `play_war1()` to get statistical results" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
" 60.693112 seconds (167.00 M allocations: 29.892 GiB, 3.56% gc time)\n" | |
] | |
} | |
], | |
"source": [ | |
"bigN = Int(1e6)\n", | |
"round_counts = UInt64[]\n", | |
"@time begin\n", | |
" open(\"war.bin\", \"w\") do f\n", | |
" for ix=1:bigN\n", | |
" round_count = play_war1()\n", | |
" write(f, round_count)\n", | |
" push!(round_counts, round_count)\n", | |
" end\n", | |
" end\n", | |
"end" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Plot statistical results" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [ | |
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"</g>\n", | |
"<g clip-path=\"url(#clip3201)\">\n", | |
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}, | |
"execution_count": 6, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"p = histogram(round_counts, bins=100, legend=false)\n", | |
"xlabel!(p, \"num rounds [ mean=$(mean(round_counts)), N=$(length(round_counts)) ]\");\n", | |
"ylabel!(p, \"num games\"), title!(p, \"Histogram of Number of Rounds of War\")\n", | |
"xlims!(p, 0, 200)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
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